MHD flows given to be unsteady with free convection, in addition toheat transfer through stretching plate held vertically in medium with permeable nature, facing radiation and Joule’s effect have been examined. Under usual boussinesq approximation, governing equations pertaining to motion and energy have been determined and converted to first order ordinary differential equations applying similarity transformation. Solvedthese equations numerically usingNewton’s iterative method as well as Runge-Kutta method. Computed the values of velocity including temperature taking help of Matlab. Analyzed through graphs the impact of Reynolds, Grashof, Hartmann and Eckert numbers, and Radiation and permeability parameters on the velocity as well as temperature field.